The scaling of the pion couplings follows from naive dimensional analysis and is confirmed by a lattice QCD calculation [1]}.
On the other hand, the scaling of the \(N\!N\)  couplings follows from the RGE in
chiral EFT [2]}, which we report here for completeness in terms of the
rescaled couplings \(\tilde{g}_{4,5}^{NN}\)  defined by \(g_{4,5}^{NN} = (m_N C/(4 \pi ))^2 \, \tilde{g}_{4,5}^{NN}\) :
\(\frac{d \, \tilde{g}_{4,5}^{NN} }{d \log \nu _\chi } = \frac{g_A^2}{4} \, g_{4,5}^{\pi \pi }\,.\) 
